In June, the U.S. carmaker had said it would close the plant if no buyer could be found for the site, which employs 900 workers.
"I hope we can reach a deal before end-October," Le Maire said after meeting with staff representatives in Bordeaux.
Punch Powerglide was a "credible, solid buyer" but had yet to detail its plans and production forecasts for Blanquefort, Le Maire said.
(Reporting by Claude Canellas, Writing by Dominique Vidalon; Editing by Laurence Frost)